Apparently, the federal government does know how to make a profit. Or, as Sen. Elizabeth Warren, D-Mass., has said in arguing for a cut in interest rates on student loans: "obscene profits."

During a July 8 floor speech Warren said, "While students are paying more, the federal government is boosting its own profits -- $51 billion from our student loan programs in 2013 alone."

But the numbers look dramatically different -- tens of billions of dollars different -- depending on which arcane method of accounting you use.

Lacey Rose, Warren's press secretary, was quick to turn up a source for this figure: the nonpartisan Congressional Budget Office. She pointed us to a CBO spreadsheet showing that outlays in the student loan program will be a negative $51 billion (in other words, a gain for the government). This figure includes $15 billion from a re-estimate of the cost of the student loans disbursed in previous years.

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A technical point: These are actually "negative subsidies," not profits as one would understand in the business world.

But here's the bigger problem: CBO itself says that it doesn't like these figures because they underestimate the cost of the loans to the American taxpayer.

By law, CBO must abide by rules established by the Federal Credit Reform Act of 1990, meaning that the cost of the loan is recorded in the federal budget the year the loan is made, with the cash flows discounted to a present value using interest rates on Treasury securities. There's now a large gap between the cost of student-loan rates (6.8 percent or 7.9 percent, unless Congress acts) and the rates on 10-year Treasury notes (estimated to be 2.1 percent), so voila, big "negative subsidies" are recorded.

Before the 1990 law was passed, the government simply tallied only the outlays and receipts for federal loans. That was considered too simplistic because it masked long-term costs, according to the Congressional Research Service.

But CBO says the post-1990 accounting method obscures tens of billions of dollars in potential losses. In particular, CBO says the current rules do not "consider some costs borne by the government," such as fully accounting for the risk of default.

So CBO has offered arguments for replacing the current accounting method with what it calls "fair-value accounting." Essentially, this approach would assess the risk as private firms would if they made the same types of loans.

"None of the differences between the federal government and private investors changes the fact that investments with returns that are correlated with the performance of the economy as a whole are risky in a way that other investments are not," CBO said. "Federal credit programs expose taxpayers to that market risk."

Last month, CBO issued fair-value estimates for virtually every federal credit program, including the subsidized Stafford loans that were the subject of congressional debate last week. The spreadsheet CBO included as part of the report makes for scary reading.

Under the mandated accounting approach, the federal government is estimated to gain $184 billion from issuing federal student loans between 2013 and 2023, CBO says. But under fair-market accounting, the government would lose $95 billion in the same period.

In other words, that's swing of nearly $280 billion depending on which accounting method you use.

The CBO's spreadsheet, meanwhile, shows that the Stafford loan program in 2013, now pegged to earn $4.6 billion in "profit," would actually lose $3.5 billion under fair-value accounting. Presumably those losses would climb sharply if interest rates were cut as Warren demands. (She would drop the rate to as low as 0.75 percent.)

Obviously, when so much money is at stake, people disagree vehemently over this issue. Adjusting the accounting rules means less money in the budget for other programs.

The left-leaning Center for American Progress has labeled the fair-value concept as "dangerous," saying it would create phantom budget deficits. Critics maintain also that the federal government is significantly different from private firms, with more tools at its disposal to recover defaulted debts.

Paul van de Water, who worked on the issue at CBO and is now at the Center on Budget and Policy Priorities, noted that the current system allows for annual re-estimates to account for what happened to the loans, which is why an additional $15 billion turned up in the accounts this year.

Still, Congress mandated that fair-value accounting be used to score policies related to Fannie Mae and Freddie Mac, as well as the Troubled Assets Relief Program. (Warren headed the TARP congressional oversight board.) The Financial Economists Roundtable has also issued a statement urging a shift to fair-value accounting.

"The Congressional Budget Office projects that the government will make $51 billion on this year's student loans," Rose said. "Those projections are done in accordance with rules laid out by Congress -- rules that have been in place for estimates of federal credit programs for more than 20 years, and rules that have been shown to reasonably measure government costs from these programs during that time. While House Republicans and other opponents of real reform may seek to change accounting rules to paper over federal profits on student loans, the only effective way to reduce them in the real world is to bring down interest rates on student loans."

We obviously are not going to take a position on the correct accounting method. And ordinarily a CBO projection is worth its weight in gold. But this is an unusual situation.

The CBO clearly has concerns about the method mandated by Congress -- and the differences over the next 11 years are stunning. Yet Warren has seized on the $51 billion figure to argue for a dramatic cut in student loan rates, making it the centerpiece of her floor speech.

The debate may be arcane, but she and other Democrats should use more caution in citing these figures -- especially when the source Warren cites, CBO, says it may not be money in the bank.